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Local Risk-Minimization With Multiple Assets Under Illiquidity With Applications In Energy Markets

Author

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  • PANAGIOTIS CHRISTODOULOU

    (Department of Mathematics, University of Munich, Theresienstraße 39, 80333 Munich, Germany)

  • NILS DETERING

    (Department of Statistics & Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA)

  • THILO MEYER-BRANDIS

    (Department of Mathematics, University of Munich, Theresienstraße 39, 80333 Munich, Germany)

Abstract

We propose a hedging approach for general contingent claims when liquidity is a concern and trading is subject to transaction cost. Multiple assets with different liquidity levels are available for hedging. Our risk criterion targets a tradeoff between minimizing the risk against fluctuations in the stock price and incurring low liquidity costs. We work in an arbitrage-free setting assuming a supply curve for each asset. In discrete time, we prove the existence of a locally risk-minimizing strategy under mild conditions on the price process. Under stochastic and time-dependent liquidity risk we give a closed-form solution for an optimal strategy in the case of a linear supply curve model. Finally we show how our hedging method can be applied in energy markets where futures with different maturities are available for trading. The futures closest to their delivery period are usually the most liquid but depending on the contingent claim not necessarily optimal in terms of hedging. In a simulation study, we investigate this tradeoff and compare the resulting hedge strategies with the classical ones.

Suggested Citation

  • Panagiotis Christodoulou & Nils Detering & Thilo Meyer-Brandis, 2018. "Local Risk-Minimization With Multiple Assets Under Illiquidity With Applications In Energy Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-44, June.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:04:n:s0219024918500280
    DOI: 10.1142/S0219024918500280
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    References listed on IDEAS

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    1. Emmanuel Gobet & Isaque Pimentel & Xavier Warin, 2020. "Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations," Finance and Stochastics, Springer, vol. 24(3), pages 633-675, July.

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